I think this might be an unmanaged switch, at least the installation guide says that on the first page. "Unmanaged Desktop PoE+ Switch "
OP mentions he has a "TL-SG1210P", but maybe double check you don't have the TL-SG1210MP which in the install manual talks about having a feature called "Isolation" that basically blocks all traffic between the individual ports (only traffic from port to uplink works).
I've never had an unmanaged switch not just be plug and play, so if the problem isn't related to isolation feature maybe you just have bad cable or switch itself (especially if you haven't ever had it work out of the box). I would focus on whether you can get two NON-CAMERA, already working devices talking to each other through the switch first, as the default IP of a new camera might add a wildcard you don't need to the initial troubleshooting to make sure the switch is working good. Then proceed with the "one cam at a time" approach. I personally add the camera default subnet to the network card in the PC manually as an additional network, and then connect the camera and pc with a cable (thereby removing the switch from causing any problems during initial setup).